Problem 52779. Easy Sequences 25: Product of Series

Created by Ramon Villamangca

Solve Later

{"parts":[{"partUri":"/matlab/document.xml","contentType":"application/vnd.mathworks.matlab.code.document+xml","content":"<?xml version=\"1.0\" encoding=\"UTF-8\"?><w:document xmlns:w=\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\"><w:body><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>The function 'P(n)' is defined as the series product:</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>                            </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"true\"/></w:customXmlPr><w:r><w:t>P(n)=\\prod_{k=2}^{n}\\frac{T(k)}{T(k)-1}</w:t></w:r></w:customXml></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>where 'T(n)' is the triangular sum:</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>                            </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"true\"/></w:customXmlPr><w:r><w:t>T(n) = 1 + 2 + 3 + 4 + ...+n</w:t></w:r></w:customXml></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>It can be proven that P(n) is convergent, with:</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>                            </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"true\"/></w:customXmlPr><w:r><w:t>\\lim_{n\\rightarrow \\infty}P(n) = 3</w:t></w:r></w:customXml></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:rPr><w:b/></w:rPr><w:t>Write a function that outputs the integer value of 'n' when '3 - P(n)' </w:t></w:r><w:r><w:rPr><w:b/><w:u/></w:rPr><w:t>first</w:t></w:r><w:r><w:rPr><w:b/></w:rPr><w:t> becomes less than or equal to a given tolerance 't'.</w:t></w:r></w:p></w:body></w:document>","relationship":null}],"relationships":[{"relationshipType":"http://schemas.mathworks.com/matlab/code/2013/relationships/document","target":"/matlab/document.xml","relationshipId":"rId1"}]}

<div style = "text-align: start; line-height: 20.440000534057617px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: normal; text-decoration: none; white-space: normal; "><div style="block-size: 256px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; vertical-align: baseline; "><div style="block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; "><span style="">The function 'P(n)' is defined as the series product:</span></span></div><div style="block-size: 46px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; "><span style="">                            </span></span><span style="vertical-align:-17px"><img src="data:image/png;base64,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" width="124.5" height="46" style="width: 124.5px; height: 46px;"></span></div><div style="block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; "><span style="">where 'T(n)' is the triangular sum:</span></span></div><div style="block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; "><span style="">                            </span></span><span style="vertical-align:-5px"><img src="data:image/png;base64,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" width="184" height="19" style="width: 184px; height: 19px;"></span></div><div style="block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; "><span style="">It can be proven that P(n) is convergent, with:</span></span></div><div style="block-size: 30px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; "><span style="">                            </span></span><span style="vertical-align:-15px"><img src="data:image/png;base64,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" width="83.5" height="29" style="width: 83.5px; height: 29px;"></span></div><div style="block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; text-align: left; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; "><span style="font-weight: bold; ">Write a function that outputs the integer value of 'n' when '3 - P(n)' </span></span><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; "><span style="font-weight: bold; text-decoration: underline; text-decoration-line: underline; ">first</span></span><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; "><span style="font-weight: bold; "> becomes less than or equal to a given tolerance 't'.</span></span></div></div></div>

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Problem 52779. Easy Sequences 25: Product of Series

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